The graph of dT / dx is shown below. At approximatel x = 6.6, the first derivative is equal to zero; below that value it is negative and above that same value it is positive. Hence T has a minimum value at around x = 6.6. Let us find the exact value by calculation

METHOD 2: We "construct a virtual house" (projection) H on the other side of the river and then for the distance d + D to be minimum we need to have the points H, O and F to be collinear since the shortest distance between two points is along a straight line. For these points to be on the same line angle HOH' have to be equal (in size) to angle FOF' and the tangent of the two angles have to be equal. Hence